Heat broiler with rack 4 inches from the heat.
Rinse salmon and pat dry with paper towels. Place salmon on a broiler pan and drizzle 2 tablespoons of lemon juice over the top. Season with salt and pepper. Broil until salmon is just cooked but still moist, 8 to 9 minutes. Remove the salmon's skin.
Meanwhile, in a medium bowl, stir together the mustard, remaining 2 tablespoons lemon juice, oil, dill, and basil. Spoon the sauce over the salmon and serve immediately.